Simply put, net neutrality is a network design paradigm that argues for broadband network providers to be completely detached from what information is sent over their networks. 
In essence, it argues that no bit of information should be prioritized over another. This principle implies that an information network such as the internet is most efficient and useful to the public when it is less focused on a particular audience and instead attentive to multiple users.
To draw a simple example, take two content providers such as the Verizon website and the University of California website. If net neutrality were upheld, both entities would pay their monthly fees to the network provider and if all else equal, any bit of information from the Verizon website will make the same trek as one from say the UC Berkeley website. There would be no roadblocks or shortcuts any of the websites can take to make the end user desire their content more. However, without a neutral stance in what is carried over their pipes, network providers can choose to discriminate and decide how fast data will be transmitted and at what quality. So in our example, say Verizon (which is also a network provider) chooses to prioritize their data over that of UC Berkeley. Information from Verizon will then be more desirable to the end user since it is so much faster than the UC website. The problem then arises when Verizon is trying to promote something opposed to that of the beliefs of the University of California. Is it fair that Verizon has these advantages over the university? What would happen if network providers bar content providers that they think have a conflict of interest from using higher speed networks? What if the network providers degrade the service of specific content providers? These are just some of the many questions that plague the net neutrality issue.
The overall story of net neutrality is summed up nicely in this video:
The neutrality principle did not originate nor is it limited to the internet. Other networks that people use every day rely on this idea. Take, for example, the electric network grid. It doesn’t matter what you plug into your electrical outlets at home, they all get access to the same electricity. The fundamental rule behind this is that no discrimination exists between any devices that you plug in; they all work equally well. Some have argued that this idea has been around since the 1800s and the age of telegraphs.
...messages received from any individual, company, or corporation, or from any telegraph lines connecting with this line at either of its termini, shall be impartially transmitted in the order of their reception, excepting that the dispatches of the government shall have priority.
– An act to facilitate communication between the Atlantic and Pacific states by electric telegraph., June 16, 1860
This essentially stated that all messages transmitted must be transmitted in the order in which they were received and cannot be subject to discrimination. The point to this is that the principle of net neutrality is not new.
A neutral network might be designed without legal prodding – as in the original internet. In an ideal world, either competition or enlightened self-interest might drive carriers to design neutral networks. Creativity, innovation and a free and open marketplace are all at stake in this fight"
